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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 463680bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 463680.bf1 | 463680bf1 | \([0, 0, 0, -37998588, -86840022512]\) | \(508017439289666674384/21234429931640625\) | \(253622672100000000000000\) | \([2]\) | \(55050240\) | \(3.2557\) | \(\Gamma_0(N)\)-optimal |
| 463680.bf2 | 463680bf2 | \([0, 0, 0, 18251412, -321987522512]\) | \(14073614784514581404/945607964406328125\) | \(-45177124031837844480000000\) | \([2]\) | \(110100480\) | \(3.6023\) |
Rank
sage: E.rank()
The elliptic curves in class 463680bf have rank \(0\).
Complex multiplication
The elliptic curves in class 463680bf do not have complex multiplication.Modular form 463680.2.a.bf
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
